Finite Group Databasebeta

← #6393387

Subgroups — #6393387

Order 512.

3726 conjugacy classes of subgroups.

The subgroup lattice has 895 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3520C211yesmaximal, characteristic
2C2×#2974C211yesmaximal, characteristic, complemented
3C2×D4×C4⋊C4C211yesmaximal, characteristic, complemented
4#22504C212yesmaximal, complemented
5#22491C214yesmaximal, complemented
6#22485C212yesmaximal, complemented
7#22431C212yesmaximal, complemented
8#22421C214yesmaximal, complemented
9D4×#103C212yesmaximal, complemented
10#21867C211yesmaximal, characteristic, complemented
11#21860C211yesmaximal, characteristic, complemented
12#21765C212yesmaximal, complemented
13#21763C212yesmaximal, complemented
14#21394C211yesmaximal, characteristic, complemented
15#21388C211yesmaximal, characteristic, complemented
16#20909C212yesmaximal, complemented
17C2×#1872C212yesmaximal, complemented
18#3520—28no—
19#3520C4116yescomplemented
20C2×#556C2211yescharacteristic
21C2×#554—21no—
22C2×#552C2212yes—
23C2×#551—22no—
24C2×D4×Q8C2211yescharacteristic
25C2×#548C2212yes—
26C2×#547C2211yescharacteristic
27C2×#547C2211yescharacteristic
28C2×#546—21no—
29C2×#542—21no—
30C2×#539—22no—
31C2×#533C2211yescharacteristic
32C2×#529C2211yescharacteristic
33C2×#525C2212yes—
34C22×C22⋊Q8C2212yes—
35C2×#520—21no—
36C22×C4×D4—21no—
37C22×C4×D4C2211yescharacteristic
38C23×C4⋊C4C2212yes—
39#2974—28no—
40C2×#436C2212yes—
41C2×#435C2214yes—
42C2×C8×D4C2212yes—
43C2×#432C2211yescharacteristic
44C2×#431C2211yescharacteristic
45C2×#417C2214yescomplemented
46C22×#103C2214yescomplemented
47C2×#407C2212yes—
48C22×C22⋊C8C2212yes—
49D4×C4⋊C4—21no—
50D4×C4⋊C4—22no—
51D4×C4⋊C4—21no—
52D4×C4⋊C4C2212yes—
53D4×C4⋊C4C2214yes—
54D4×C4⋊C4C2212yes—
55C2×#389—21no—
56C2×#385—22no—
57C2×#384C2211yescharacteristic
58C2×#380C2212yes—
59C2×C4×C4⋊C4C2211yescharacteristic
60#1992C2212yescomplemented
61#1990C2212yescomplemented
62#1989C2212yescomplemented
63#1988C2212yescomplemented
64#1983C2212yescomplemented
65#1981C2212yescomplemented
66#1959C2212yescomplemented
67#1956C2212yescomplemented
68#1894C2214yescomplemented
69#1894C2214yescomplemented
70#1893C2214yescomplemented
71#1892C2214yescomplemented
72#1874C2211yescharacteristic
73#1874C2212yes—
74#1874C2211yescharacteristic
75#1874C2214yescomplemented
76#1872C2212yes—
77#1872C2212yes—
78#1872C2211yescharacteristic
79#1872C2212yes—
80#1872C2212yes—
81#1872C2211yescharacteristic
82#1872C2212yes—
83#1872C2214yescomplemented
84#1872C2214yescomplemented
85#1872C2214yescomplemented
86#1825C2214yescomplemented
87#1823C2214yescomplemented
88#1803C2214yescomplemented
89#1803C2212yescomplemented
90#1802C2212yescomplemented
91#1788C2214yescomplemented
92#1787C2214yescomplemented
93#1763C2214yescomplemented
94C4×#103C2212yescomplemented
95C4×#102C2212yescomplemented
96#1736C2214yescomplemented
97C2×#340C2214yescomplemented
98C22×#41—21no—
99C22×#41C2312yes—
100C23×Q8C2312yes—
101C23×D4D411yescharacteristic
102C24×C4—22no—
103C24×C4C2312yes—
104C22×M16C2314yes—
105C23×C8C2314yes—
106#556—24no—
107#556C2×C418yescomplemented
108#554—216no—
109#552—28no—
110#552C2×C4116yescomplemented
111#551—232no—
112D4×Q8—24no—
113D4×Q8C2×C418yescomplemented
114#548—28no—
115#548C2×C4116yescomplemented
116#547—24no—
117#547—24no—
118#547C2×C418yescomplemented
119#547C2×C418yescomplemented
120#546—216no—
121#542—216no—
122#539—232no—
123#533—24no—
124#533C2×C418yescomplemented
125C2×C4⋊Q8—21no—
126C2×C4⋊Q8C2311yescharacteristic
127C2×C4⋊Q8C2311yescharacteristic
128#529—24no—
129#529C2×C418yescomplemented
130C2×#126—22no—
131C2×#126—22no—
132C2×#126—21no—
133C2×#125—22no—
134C2×#125—21no—
135C2×#125C2311yescharacteristic
136C2×#124—21no—
137C2×#124—22no—
138C2×#124C2311yescharacteristic
139#525—28no—
140#525C2×C4116yescomplemented
141C2×#123—22no—
142C2×#123—22no—
143C2×#123—21no—
144C2×#123—22no—
145C2×#123—22no—
146C2×C22⋊Q8—22no—
147C2×C22⋊Q8—22no—
148C2×C22⋊Q8—28no—
149C2×C22⋊Q8—21no—
150C2×C22⋊Q8—22no—
151C2×C22⋊Q8—21no—
152C2×C22⋊Q8—22no—
153C2×C22⋊Q8C2×C4116yescomplemented
154C2×C22⋊Q8C2311yescharacteristic
155C2×C22⋊Q8C2312yes—
156C2×C22⋊Q8C2312yes—
157C2×C22⋊Q8C2312yes—
158C2×C22⋊Q8C2312yes—
159C2×#121—22no—
160C2×#121—21no—
161C2×#121C2311yescharacteristic
162C2×#121C2312yes—
163C2×#120—22no—
164#520—216no—
165C2×C4×Q8—21no—
166C2×C4×Q8—21no—
167C2×C4×Q8C2311yescharacteristic
168C2×C4×Q8C2312yes—
169C2×C4×D4—21no—
170C2×C4×D4—22no—
171C2×C4×D4—22no—
172C2×C4×D4—21no—
173C2×C4×D4—24no—
174C2×C4×D4—22no—
175C2×C4×D4—22no—
176C2×C4×D4—22no—
177C2×C4×D4—48no—
178C2×C4×D4C2×C418yes—
179C2×C4×D4D418yes—
180C2×C4×D4D411yescharacteristic
181C2×C4×D4D412yes—
182C2×C4×D4D411yescharacteristic
183C2×C4×D4C2311yescharacteristic
184C2×C4×D4C2311yescharacteristic
185C2×C4×D4C2312yes—
186C2×C4×D4C2311yescharacteristic
187C2×#117—21no—
188C2×#117—22no—
189C2×#117—21no—
190C2×#117C2312yes—
191C22×C4⋊C4—22no—
192C22×C4⋊C4—21no—
193C22×C4⋊C4—22no—
194C22×C4⋊C4—22no—
195C22×C4⋊C4—22no—
196C22×C4⋊C4—21no—
197C22×C4⋊C4—21no—
198C22×C4⋊C4—48no—
199C22×C4⋊C4D411yescharacteristic
200C22×C4⋊C4C2311yescharacteristic
201C22×C4⋊C4C2314yes—
202C22×C4⋊C4C2314yes—
203C22×C4⋊C4C2312yes—
204C22×C4⋊C4C2312yes—
205C22×C4⋊C4C2311yescharacteristic
206C22×C22⋊C4—22no—
207C22×C22⋊C4—22no—
208C22×C22⋊C4D412yes—
209C22×C42—21no—
210C22×C42C2311yescharacteristic
211#436—28no—
212#435—216no—
213C8×D4—28no—
214#432—24no—
215#431—24no—
216C2×C4⋊C8C2312yes—
217C2×C4⋊C8C2312yes—
218#417—48no—
219C2×#103—48no—
220C2×#103C2312yes—
221C2×#103C2314yes—
222C2×#103C2314yes—
223C2×#103C2314yes—
224C2×#103C2314yes—
225C2×#103C2314yes—
226C2×#103C2312yes—
227C2×#102C2312yes—
228C2×#102C2314yes—
229C2×#102C2312yes—
230#407—28no—
231C2×C22⋊C8—28no—
232C2×C22⋊C8C2314yes—
233C2×C22⋊C8C2314yes—
234C2×C22⋊C8C2311yescharacteristic
235C2×C22⋊C8C2312yes—
236C2×C22⋊C8C2311yescharacteristic
237C2×#97C2312yes—
238C2×C4×C8C2312yes—
239#389—22no—
240#389—24no—
241#389—22no—
242#385—24no—
243#385—24no—
244#385—24no—
245#385—24no—
246#384—21no—
247#384—21no—
248#384C2312yes—
249#384C2312yes—
250#380—22no—
251#380—22no—
252#380C2314yes—
253#380C2314yes—
254C4×C4⋊C4—21no—
255C4×C4⋊C4—21no—
256C4×C4⋊C4C2312yes—
257C4×C4⋊C4C2312yes—
258C2×#95—21no—
259C2×#95—22no—
260#340C2314yes—
261#340C2314yes—
262#340C2314yes—
263#340C2314yes—
264#340C2312yes—
265#340C2314yes—
266#340C2312yes—
267#340C2312yes—
268#340C2314yes—
269#340C2312yes—
270C25C2×D412yes—
271C2×#41—28no—
272C2×#41—24no—
273C2×#41—44no—
274C2×#41—44no—
275C2×#41—44no—
276C2×#41—44no—
277C2×#41C22×C418yescomplemented
278C22×Q8—21no—
279C22×Q8—22no—
280C22×Q8—24no—
281C22×Q8—44no—
282C22×Q8—44no—
283C22×Q8C22×C418yescomplemented
284C22×Q8C2411yescharacteristic
285C22×Q8C2412yes—
286C22×D4—24no—
287C22×D4—24no—
288C22×D4—21no—
289C22×D4—22no—
290C22×D4—22no—
291C22×D4C22⋊C418yes—
292C22×D4C2×D412yes—
293C22×D4C2×D411yescharacteristic
294C22×D4C2×D411yescharacteristic
295C22×D4C2411yescharacteristic
296C23×C4—22no—
297C23×C4—21no—
298C23×C4—22no—
299C23×C4—21no—
300C23×C4—22no—
301C23×C4—21no—
302C23×C4—22no—
303C23×C4—24no—
304C23×C4—24no—
305C23×C4—44no—
306C23×C4—44no—
307C23×C4—48no—
308C23×C4—48no—
309C23×C4—84no—
310C23×C4C22×C418yes—
311C23×C4C2×D411yescharacteristic
312C23×C4C2×D411yescharacteristic
313C23×C4C2×D412yes—
314C23×C4C2×D412yes—
315C23×C4C2×D412yes—
316C23×C4C2×D418yes—
317C23×C4C2411yescharacteristic
318C23×C4C2412yes—
319C23×C4C2412yes—
320C2×M16—28no—
321C2×M16—44no—
322C2×M16—44no—
323C22×C8—28no—
324C22×C8—44no—
325C22×C8—44no—
326C22×C8C2412yes—
327C22×C8C2414yes—
328C22×C8C2412yes—
329C4⋊Q8—28no—
330C4⋊Q8—22no—
331C4⋊Q8—22no—
332C4⋊Q8C22×C414yescomplemented
333C4⋊Q8C22×C414yescomplemented
334#126—216no—
335#126—216no—
336#126—28no—
337#125—216no—
338#125—28no—
339#125—22no—
340#125C22×C414yescomplemented
341#124—28no—
342#124—216no—
343#124—22no—
344#124C22×C414yescomplemented
345#123—216no—
346#123—216no—
347#123—28no—
348#123—216no—
349#123—216no—
350C22⋊Q8—216no—
351C22⋊Q8—216no—
352C22⋊Q8—28no—
353C22⋊Q8—22no—
354C22⋊Q8—24no—
355C22⋊Q8—24no—
356C22⋊Q8—24no—
357C22⋊Q8—24no—
358C22⋊Q8—216no—
359C22⋊Q8—28no—
360C22⋊Q8—216no—
361C22⋊Q8C22×C414yes—
362C22⋊Q8C22×C418yes—
363C22⋊Q8C22×C418yescomplemented
364C22⋊Q8C22×C418yescomplemented
365C22⋊Q8C22×C418yescomplemented
366#121—216no—
367#121—28no—
368#121—22no—
369#121—24no—
370#121C22×C414yes—
371#121C22×C418yescomplemented
372#120—216no—
373C4×Q8—28no—
374C4×Q8—28no—
375C4×Q8—22no—
376C4×Q8—24no—
377C4×Q8C22×C414yescomplemented
378C4×Q8C22×C418yescomplemented
379C4×D4—28no—
380C4×D4—216no—
381C4×D4—216no—
382C4×D4—28no—
383C4×D4—216no—
384C4×D4—22no—
385C4×D4—416no—
386C4×D4—48no—
387C4×D4—48no—
388C4×D4C22⋊C418yes—
389C4×D4C22⋊C4116yes—
390C4×D4C22⋊C418yes—
391C4×D4C22×C414yes—
392C4×D4C22×C414yes—
393C4×D4C22×C418yes—
394C4×D4C22×C414yescomplemented
395C4×D4C2×D414yes—
396C4×D4C2×D414yes—
397C4×D4C2×D418yes—
398#117—28no—
399#117—24no—
400#117—216no—
401#117—28no—
402#117C22×C418yescomplemented
403C2×C4⋊C4—216no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—24no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—28no—
420C2×C4⋊C4—24no—
421C2×C4⋊C4—28no—
422C2×C4⋊C4—28no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—24no—
425C2×C4⋊C4—24no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—44no—
432C2×C4⋊C4—44no—
433C2×C4⋊C4—44no—
434C2×C4⋊C4—42no—
435C2×C4⋊C4—48no—
436C2×C4⋊C4—48no—
437C2×C4⋊C4—48no—
438C2×C4⋊C4—44no—
439C2×C4⋊C4—82no—
440C2×C4⋊C4C22⋊C418yes—
441C2×C4⋊C4C22×C418yescomplemented
442C2×C4⋊C4C2×D411yescharacteristic
443C2×C4⋊C4C2×D412yes—
444C2×C4⋊C4C2×D411yescharacteristic
445C2×C4⋊C4C2414yes—
446C2×C4⋊C4C2412yes—
447C2×C4⋊C4C2411yescharacteristic
448C2×C4⋊C4C2412yes—
449C2×C4⋊C4C2411yescharacteristic
450C2×C4⋊C4C2412yes—
451C2×C22⋊C4—216no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—22no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—22no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—24no—
464C2×C22⋊C4—24no—
465C2×C22⋊C4—48no—
466C2×C22⋊C4C22⋊C4116yes—
467C2×C22⋊C4C2×D412yes—
468C2×C22⋊C4C2×D412yes—
469C2×C22⋊C4C2×D412yes—
470C2×C22⋊C4C2×D412yes—
471C2×C42—22no—
472C2×C42—22no—
473C2×C42—21no—
474C2×C42—22no—
475C2×C42—22no—
476C2×C42—44no—
477C2×C42C22×C414yes—
478C2×C42C2×D411yescharacteristic
479C2×C42C2×D411yescharacteristic
480C2×C42C2×D414yes—
481C2×C42C2411yescharacteristic
482C2×C42C2411yescharacteristic
483C4⋊C8—24no—
484C4⋊C8—24no—
485#103—24no—
486#103—28no—
487#103—44no—
488#103—44no—
489#103—42no—
490#103—44no—
491#103—44no—
492#102—24no—
493#102—42no—
494#102—44no—
495C22⋊C8—22no—
496C22⋊C8—24no—
497C22⋊C8—28no—
498C22⋊C8—22no—
499C22⋊C8—28no—
500#97—24no—
501C4×C8—24no—
502#95—22no—
503#95—22no—
504#95—24no—
505#95—24no—
506C24—24no—
507C24—24no—
508C24—24no—
509C24—24no—
510C24—21no—
511C24—42no—
512C24—42no—
513C24C2×C22⋊C418yes—
514C24C22×D412yes—
515C24C22×D412yes—
516C24C22×D411yescharacteristic
517#41—416no—
518#41—432no—
519#41—88no—
520C2×Q8—24no—
521C2×Q8—28no—
522C2×Q8—21no—
523C2×Q8—22no—
524C2×Q8—22no—
525C2×Q8—24no—
526C2×Q8—22no—
527C2×Q8—24no—
528C2×Q8—416no—
529C2×Q8—42no—
530C2×Q8—42no—
531C2×Q8—82no—
532C2×Q8—82no—
533C2×Q8—88no—
534C2×Q8C23×C412yes—
535C2×Q8C23×C414yes—
536C2×D4—24no—
537C2×D4—24no—
538C2×D4—232no—
539C2×D4—24no—
540C2×D4—28no—
541C2×D4—28no—
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—21no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—44no—
548C2×D4—44no—
549C2×D4—42no—
550C2×D4—42no—
551C2×D4—82no—
552C2×D4—82no—
553C2×D4C2×C22⋊C418yes—
554C2×D4C2×C22⋊C414yes—
555C2×D4C2×C22⋊C414yes—
556C2×D4AGL(1,ℤ/8)14yes—
557C2×D4#13714yes—
558C2×D4C23×C412yes—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—24no—
565C22×C4—24no—
566C22×C4—22no—
567C22×C4—24no—
568C22×C4—24no—
569C22×C4—24no—
570C22×C4—28no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—28no—
578C22×C4—24no—
579C22×C4—28no—
580C22×C4—22no—
581C22×C4—24no—
582C22×C4—416no—
583C22×C4—416no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—48no—
591C22×C4—48no—
592C22×C4—42no—
593C22×C4—44no—
594C22×C4—44no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—44no—
600C22×C4—44no—
601C22×C4—42no—
602C22×C4—48no—
603C22×C4—48no—
604C22×C4—44no—
605C22×C4—42no—
606C22×C4—82no—
607C22×C4—82no—
608C22×C4—84no—
609C22×C4—84no—
610C22×C4—82no—
611C22×C4—82no—
612C22×C4—832no—
613C22×C4C2×C22⋊C414yes—
614C22×C4C2×C22⋊C414yes—
615C22×C4C2×C22⋊C418yes—
616C22×C4C2×C22⋊C418yes—
617C22×C4C2×C22⋊C418yes—
618C22×C4C23×C412yes—
619C22×C4C23×C414yes—
620C22×C4C23×C414yes—
621C22×C4C22×D411yescharacteristic
622C22×C4C22×D412yes—
623C22×C4C22×D411yescharacteristic
624C22×C4C22×D412yes—
625C22×C4C22×D411yescharacteristic
626C22×C4C22×D411yescharacteristic
627C22×C4C22×D412yes—
628C22×C4C22×D414yes—
629C22×C4C22×D414yes—
630C22×C4C22×D411yescharacteristic
631C22×C4C2511yescharacteristic
632M16—88no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—24no—
636C2×C8—22no—
637C2×C8—24no—
638C2×C8—22no—
639C2×C8—22no—
640C2×C8—24no—
641C2×C8—22no—
642C2×C8—88no—
643C4⋊C4—24no—
644C4⋊C4—24no—
645C4⋊C4—28no—
646C4⋊C4—24no—
647C4⋊C4—28no—
648C4⋊C4—28no—
649C4⋊C4—28no—
650C4⋊C4—24no—
651C4⋊C4—24no—
652C4⋊C4—24no—
653C4⋊C4—28no—
654C4⋊C4—24no—
655C4⋊C4—28no—
656C4⋊C4—24no—
657C4⋊C4—21no—
658C4⋊C4—22no—
659C4⋊C4—21no—
660C4⋊C4—22no—
661C4⋊C4—24no—
662C4⋊C4—24no—
663C4⋊C4—22no—
664C4⋊C4—22no—
665C4⋊C4—48no—
666C4⋊C4—48no—
667C4⋊C4—42no—
668C4⋊C4—44no—
669C4⋊C4—44no—
670C4⋊C4—44no—
671C4⋊C4—82no—
672C4⋊C4—82no—
673C4⋊C4C2×C22⋊C414yes—
674C4⋊C4C2×C22⋊C418yes—
675C4⋊C4C2×C22⋊C414yes—
676C4⋊C4C23×C412yes—
677C4⋊C4C23×C414yes—
678C4⋊C4C23×C412yes—
679C4⋊C4H(5,𝔽2)14yes—
680C22⋊C4—24no—
681C22⋊C4—28no—
682C22⋊C4—28no—
683C22⋊C4—28no—
684C22⋊C4—28no—
685C22⋊C4—28no—
686C22⋊C4—24no—
687C22⋊C4—24no—
688C22⋊C4—24no—
689C22⋊C4—28no—
690C22⋊C4—24no—
691C22⋊C4—48no—
692C22⋊C4—48no—
693C22⋊C4C2×C22⋊C418yes—
694C22⋊C4C2×C22⋊C418yes—
695C22⋊C4C2×C22⋊C418yes—
696C22⋊C4C2×C22⋊C418yes—
697C42—28no—
698C42—28no—
699C42—24no—
700C42—44no—
701C42—44no—
702C42C2×C22⋊C414yes—
703C42C2×C22⋊C414yes—
704C42C23×C412yes—
705C42C23×C412yes—
706C42C22×D412yes—
707C42C22×D412yes—
708C23—21no—
709C23—22no—
710C23—21no—
711C23—22no—
712C23—21no—
713C23—21no—
714C23—22no—
715C23—22no—
716C23—216no—
717C23—216no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—48no—
726C23—48no—
727C23—48no—
728C23—48no—
729C23—48no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23C22×C22⋊C414yes—
737C23C22×C22⋊C414yes—
738C23C22×C22⋊C412yes—
739C23C2×AGL(1,ℤ/8)14yes—
740C23C2×#13714yes—
741C23#57712yes—
742C23#57812yes—
743C23C23×D411yescharacteristic
744Q8—24no—
745Q8—28no—
746Q8—48no—
747Q8—42no—
748Q8—44no—
749Q8—88no—
750D4—216no—
751D4—28no—
752D4—24no—
753D4—416no—
754D4—48no—
755D4—42no—
756D4—88no—
757D4#417116yescomplemented
758C2×C4—28no—
759C2×C4—21no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—21no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—28no—
772C2×C4—24no—
773C2×C4—28no—
774C2×C4—28no—
775C2×C4—28no—
776C2×C4—28no—
777C2×C4—24no—
778C2×C4—22no—
779C2×C4—24no—
780C2×C4—22no—
781C2×C4—24no—
782C2×C4—22no—
783C2×C4—24no—
784C2×C4—48no—
785C2×C4—48no—
786C2×C4—48no—
787C2×C4—48no—
788C2×C4—416no—
789C2×C4—42no—
790C2×C4—41no—
791C2×C4—42no—
792C2×C4—41no—
793C2×C4—42no—
794C2×C4—41no—
795C2×C4—42no—
796C2×C4—41no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—48no—
802C2×C4—44no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—44no—
806C2×C4—44no—
807C2×C4—42no—
808C2×C4—88no—
809C2×C4—88no—
810C2×C4—816no—
811C2×C4—816no—
812C2×C4—84no—
813C2×C4—88no—
814C2×C4C22×C22⋊C412yes—
815C2×C4C22×C22⋊C414yes—
816C2×C4C22×C22⋊C412yes—
817C2×C4C22×C22⋊C412yes—
818C2×C4C22×C22⋊C412yes—
819C2×C4C22×C22⋊C414yes—
820C2×C4C22×C22⋊C412yes—
821C2×C4C2×AGL(1,ℤ/8)12yes—
822C2×C4C2×#13712yes—
823C2×C4C24×C411yescharacteristic
824C2×C4C23×D411yescharacteristic
825C2×C4C2×H(5,𝔽2)12yes—
826C2×C4#58512yes—
827C8—42no—
828C8—44no—
829C8—42no—
830C22—22no—
831C22—24no—
832C22—22no—
833C22—24no—
834C22—22no—
835C22—24no—
836C22—22no—
837C22—24no—
838C22—22no—
839C22—24no—
840C22—22no—
841C22—24no—
842C22—24no—
843C22—24no—
844C22—24no—
845C22—432no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—81no—
854C22—81no—
855C22—81no—
856C22—81no—
857C22C2×#41718yes—
858C22#289814yes—
859C22C23×C22⋊C411yescharacteristic
860C22#348411yescharacteristic
861C22#348511yescharacteristic
862C22C22×AGL(1,ℤ/8)11yescharacteristic
863C22C22×#13711yescharacteristic
864C22C2×#57711yescharacteristic
865C22C2×#57811yescharacteristic
866C4—22no—
867C4—22no—
868C4—22no—
869C4—22no—
870C4—24no—
871C4—24no—
872C4—44no—
873C4—42no—
874C4—44no—
875C4—42no—
876C4—44no—
877C4—42no—
878C4—82no—
879C4—84no—
880C4C2×#41714yes—
881C4C4×H(5,𝔽2)12yes—
882C4#349612yes—
883C2—24no—
884C2—28no—
885C2—44no—
886C2—82no—
887C2#3425611yescharacteristic
888C2C22×#41711yescharacteristic
889C2C2×#289811yescharacteristic
890C2#6160011yescharacteristic
891C2#6160211yescharacteristic
892C2#6173511yescharacteristic
893C2#6173711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radicalC2×#3520C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×C4×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#2974C2semidirect
3. C2×D4×C4⋊C4C2semidirect
4. #22504C2semidirect
5. #22491C2semidirect
6. #22485C2semidirect
7. #22431C2semidirect
8. #22421C2semidirect
9. D4×#103C2semidirect
10. #21867C2semidirect
11. #21860C2semidirect
12. #21765C2semidirect
13. #21763C2semidirect
14. #21394C2semidirect
15. #21388C2semidirect
16. #20909C2semidirect
17. C2×#1872C2semidirect
19. #3520C4semidirect
45. C2×#417C22semidirect
46. C22×#103C22semidirect
60. #1992C22semidirect
61. #1990C22semidirect
62. #1989C22semidirect
63. #1988C22semidirect
64. #1983C22semidirect
65. #1981C22semidirect
66. #1959C22semidirect
67. #1956C22semidirect
68. #1894C22semidirect
69. #1894C22semidirect
70. #1893C22semidirect
71. #1892C22semidirect
75. #1874C22semidirect
83. #1872C22semidirect
84. #1872C22semidirect
85. #1872C22semidirect
86. #1825C22semidirect
87. #1823C22semidirect
88. #1803C22semidirect
89. #1803C22semidirect
90. #1802C22semidirect
91. #1788C22semidirect
92. #1787C22semidirect
93. #1763C22semidirect
94. C4×#103C22semidirect
95. C4×#102C22semidirect
96. #1736C22semidirect
97. C2×#340C22semidirect
107. #556C2×C4semidirect
110. #552C2×C4semidirect
113. D4×Q8C2×C4semidirect
115. #548C2×C4semidirect
118. #547C2×C4semidirect
119. #547C2×C4semidirect
124. #533C2×C4semidirect
129. #529C2×C4semidirect
140. #525C2×C4semidirect
153. C2×C22⋊Q8C2×C4semidirect
277. C2×#41C22×C4semidirect
283. C22×Q8C22×C4semidirect
332. C4⋊Q8C22×C4semidirect
333. C4⋊Q8C22×C4semidirect
340. #125C22×C4semidirect
344. #124C22×C4semidirect
363. C22⋊Q8C22×C4semidirect
364. C22⋊Q8C22×C4semidirect
365. C22⋊Q8C22×C4semidirect
371. #121C22×C4semidirect
377. C4×Q8C22×C4semidirect
378. C4×Q8C22×C4semidirect
394. C4×D4C22×C4semidirect
402. #117C22×C4semidirect
441. C2×C4⋊C4C22×C4semidirect
757. D4#417semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#35202
C2×#29742
C2×D4×C4⋊C42
#225042
#224912
#224852
#224312
#224212
D4×#1032
#218672
#218602
#217652
#217632
#213942
#213882
#209092
C2×#18722